Can I get anything real out of a model?

Yes, of course. If your model is good, and your spectra do contain enough information, the parameter values reflect the real values as good as they can.
Please have in mind that in many cases talking about ‘real values’ is using a model in itself. If you ask for the real value of a layer thickness, for example, your question implies that there is something like a layer with a top and a bottom end. You ignore the atomic structure and surface roughness effects, or, if not, you apply (at least in your mind) a certain roughness averaging procedure.